Twodimensional adiabatic flows on to a black hole  I. Fluid accretion
Abstract
When gas accretes on to a black hole, at a rate either much less than or much greater than the Eddington rate, it is likely to do so in an `adiabatic' or radiatively inefficient manner. Under fluid (as opposed to magnetohydrodynamic) conditions, the disc should become convective and evolve toward a state of marginal instability. We model the resulting disc structure as `gyrentropic', with convection proceeding along common surfaces of constant angular momentum, Bernouilli function and entropy, called `gyrentropes'. We present a family of twodimensional, selfsimilar models that describes the timeaveraged disc structure. We then suppose that there is a selfsimilar, Newtonian torque, which dominates the angular momentum transport and that the Prandtl number is large so that convection dominates the heat transport. The torque drives inflow and meridional circulation and the resulting flow is computed. Convective transport will become ineffectual near the disc surface. It is conjectured that this will lead to a large increase of entropy across a `thermal front', which we identify as the effective disc surface and the base of an outflow. The conservation of mass, momentum and energy across this thermal front permits a matching of the disc models to selfsimilar outflow solutions. We then demonstrate that selfsimilar disc solutions can be matched smoothly on to relativistic flows at small radius and thin discs at large radius. This model of adiabatic accretion is contrasted with some alternative models that have been discussed recently. The disc models developed in this paper should be useful for interpreting numerical, fluid dynamical simulations. Related principles to those described here may govern the behaviour of astrophysically relevant, magnetohydrodynamic disc models.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 2004
 DOI:
 10.1111/j.13652966.2004.07425.x
 arXiv:
 arXiv:astroph/0306184
 Bibcode:
 2004MNRAS.349...68B
 Keywords:

 accretion;
 accretion discs;
 black hole physics;
 hydrodynamics;
 quasars: absorption lines;
 Astrophysics
 EPrint:
 21 pages, 9 figures, submitted to Monthly Notices of the Royal Astronomical Society